# Optimal Design of Flow Control Fins for a Small Container Ship Based on Machine Learning

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## Abstract

**:**

## 1. Introduction

#### 1.1. Importance of Flow Control Fins (FCFs) in Ship Energy Efficiency

#### 1.2. Contributions

## 2. Theoretical Backgrounds

#### 2.1. Artificial Neural Network (ANN)

#### 2.2. Optimization Algorithms

#### 2.2.1. Sequential Least Squares Programming (SLSQP)

#### 2.2.2. Non-Dominated Sorting Genetic Algorithm-II (NSGA-II)

## 3. Problem Description

#### 3.1. Geometry of Target Ship and Flow Control Fins

#### 3.2. CFD Simulation for Training Data

^{®}(Cadas Co., Ltd., Changwon, Republic of Korea) The subsequent processes involved in the configuration of STAR-CCM+ and analysis automation were controlled via an in-house JavaScript code. Using a Message Passing Interface (MPI) parallel computing cluster consisting of 140 CPU cores (Intel Xeon 2.6 GHz), it took approximately 323 h to complete the 693 simulations required for the preparation of data.

## 4. Methodologies

#### 4.1. ANN-Based Prediction of Wake Distribution

#### 4.2. Selection of the Optimal Fin Position

#### 4.2.1. Single-Objective Optimization Using SLSQP

#### 4.2.2. Multi-Objective Optimization Using NSGA-II

## 5. Results

#### 5.1. Validation of CFD Analysis

#### 5.2. The ANN-Based Prediction

#### 5.3. Optimization of the Design Variables of FCFs

#### 5.3.1. Single-Objective Optimization Results

#### 5.3.2. Multi-Objective Optimization Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**A 3D volumetric views of baseline hull and propeller: (

**a**) baseline hull; (

**b**) propeller and rudder.

**Figure 7.**Pre-processing of output data for neural network: (

**a**) division on propeller disc; (

**b**) process of harmonic analysis.

**Figure 10.**Evaluation of prediction accuracy via harmonic wake distribution and axial wake distribution: (

**a**) test data No. 1; (

**b**) test data No. 2.

**Figure 12.**Evolutionary results during process of single-objective optimization: (

**a**) initial:${w}_{N}=0.247$; (

**b**) step 1: ${w}_{N}=0.249$; (

**c**) step 2: ${w}_{N}=0.242$; (

**d**) step 3: ${w}_{N}=0.225$; (

**e**) step 4: ${w}_{N}=0.225$; (

**f**) step 5: ${w}_{N}=0.240$; (

**g**) step 6: ${w}_{N}=0.236$; (

**h**) step 7: ${w}_{N}=0.226$; (

**i**) step 8: ${w}_{N}=0.225$.

**Figure 14.**Best pareto front discovered via NSGA-II: (

**a**) initial: ${w}_{N}=0.247$; (

**b**) optimal: ${w}_{N}=0.225$.

**Figure 15.**Comparison of wake distributions for initial design: (

**a**) CFD: ${w}_{N}=0.248$; (

**b**) ANN prediction: ${w}_{N}=0.247$.

**Figure 16.**Comparison of wake distributions for optimal design: (

**a**) CFD: ${w}_{N}=0.226$; (

**b**) ANN prediction: ${w}_{N}=0.225$.

**Figure 17.**Comparison between optimal wake and best case among collected data: (

**a**) bare hull: ${w}_{N}=0.275$; (

**b**) best case among 693 data: ${w}_{N}=0.232$; (

**c**) optimal FCF: ${w}_{N}=0.225$.

**Figure 19.**Comparison of pressure distribution and streamline: (

**a**) bare hull; (

**b**) the optimized FCF.

Designation | Symbol (Unit) | Full-Scale Ship |
---|---|---|

Length bet. perpendiculars | ${L}_{PP}$ (m) | 137.5 |

Breadth | $B$ (m) | 23.6 |

Draft | $T$ (m) | 7.4 |

Block coefficient | ${C}_{B}$ | 0.595 |

Propeller diameter | $D$ (m) | 5.5 |

**Table 2.**Boundary conditions for Figure 6.

Boundary Surface | Type |
---|---|

Inlet | Velocity inlet |

Outlet | Pressure outlet |

Top, bottom, side, centerplane | Symmetry |

Ship | Wall |

Item | Value |
---|---|

# of Nodes of Hidden layer—1 | 11 |

# of Nodes of Hidden layer—2 | 22 |

# of Nodes of Hidden layer—3 | 44 |

# of Nodes of Hidden layer—4 | 66 |

# of Nodes of Hidden layer—5 | 89 |

Vs [kn] | ${\mathit{C}}_{\mathit{T}\mathit{M}}\times {10}^{3}$ | ${\mathit{C}}_{\mathit{R}}\times {10}^{3}$ | ||||
---|---|---|---|---|---|---|

EXP | CFD | Difference | EXP | CFD | Difference | |

17.0 | 3.929 | 3.870 | −1.50% | 0.741 | 0.678 | −0.06 |

18.0 | 3.999 | 3.993 | −0.15% | 0.843 | 0.834 | −0.01 |

19.0 | 4.199 | 4.178 | −0.50% | 1.073 | 1.049 | −0.02 |

Bare Hull | Optimal Fin | |
---|---|---|

${C}_{VM}\times {10}^{3}$ | 3.206 | 3.207 |

${R}_{VM}$ [N] | 52.37 | 52.41 |

Bare Hull | Optimal Fin | |
---|---|---|

${C}_{VM}\times {10}^{3}$ | 3.206 | 3.203 |

${R}_{VM}$ [N] | 52.37 | 52.34 |

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**MDPI and ACS Style**

Lee, M.-K.; Lee, I.
Optimal Design of Flow Control Fins for a Small Container Ship Based on Machine Learning. *J. Mar. Sci. Eng.* **2023**, *11*, 1149.
https://doi.org/10.3390/jmse11061149

**AMA Style**

Lee M-K, Lee I.
Optimal Design of Flow Control Fins for a Small Container Ship Based on Machine Learning. *Journal of Marine Science and Engineering*. 2023; 11(6):1149.
https://doi.org/10.3390/jmse11061149

**Chicago/Turabian Style**

Lee, Min-Kyung, and Inwon Lee.
2023. "Optimal Design of Flow Control Fins for a Small Container Ship Based on Machine Learning" *Journal of Marine Science and Engineering* 11, no. 6: 1149.
https://doi.org/10.3390/jmse11061149